The concept (doctrine, dogma or theory) of the trinity didn't exist until hundreds of years after Christ. In other words, it was never taught by Yahushua, (Jesus) the Messiah. The Catholic church adopted it after much argument, at the Council of Nicaea in 325 A.D. and then amended it at the First Council of Constantinople, 381 A.D.

"The Christian doctrine of the Trinity (Latin: Trinitas, lit. 'triad', from Latin: trinus "threefold") holds that God is one God, but three coeternal consubstantial persons or hypostases—the Father, the Son (Jesus Christ), and the Holy Spirit—as "one God in three Divine persons". The three persons are distinct, yet are one "substance, essence or nature" (homoousios)" (see wikipedia)

What does that mean?

There are supposedly three persons (three beings, not three people), each person is fully God, but the three together are one God. All three are co-equal, all three are co-substantial (made of the same stuff). They are the Father, the Son, and the Holy Spirit. All God, all equal, all the same but different and make only one God.

Any discussion or teaching of the trinity likely has some sentence or phrase similar to:

"The Trinity is beyond our ability to understand." or "The Trinity is a mystery…"

That's because the doctrine of the trinity, as generally taught is illogical (impossible, as in 3=1 instead of 3=3 and 1=1). It's like the long-standing contradictory, illogical challenge "Can an all powerful God create a rock so big he can't lift it?" (Hint: he either can't make a rock that big, so is not all powerful OR if he can make a rock that big, and can't lift it, he is again not all powerful.) The Trinity doctrine is made of the same illogical, impossible ingredients.

Let's see if we can make some sense of it all.

For an excellent, long, in depth study see Is God a Trinity? on this site.
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